NF-Extend+understanding+of+fraction+equivalence+and+ordering

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. || ===‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. || Use __technology__ tools and skills to reinforce classroom concepts and activities. || ===‍‍‍‍‍‍Revised Bloom's Level of thinking === Remembering Understanding Analyzing || ===‍‍‍‍‍‍Learning Target/Task Analysis === 4.NF.1 This standard refers to visual fraction models. This includes area models, linear models (number lines) or it could be a collection/set models. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard extends the __work__ in third grade by using additional denominators (5, 10, 12, and 100). <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students can use visual models or applets to generate equivalent fractions.
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Core Standards ===
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Information Technology Standard ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">All the area models show 1/2. The second model shows 2/4 but also shows that 1/2 and 2/4 are <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">equivalent fractions because their areas are equivalent. When a horizontal line is drawn through <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the center of the model, the number of equal parts doubles and size of the parts is halved. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students will begin to notice connections between the models and fractions in the way both the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">parts and wholes are counted and begin to generate a rule for writing equivalent fractions.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">1/2 = 1/2 x 2/2 = 2/4 =

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">1/2 x 3/3 = 3/6 = 1/2 x 4/4 = 4/8 =

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Technology Connection

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NF.2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard calls students to compare fractions by creating visual fraction models or finding common denominators or numerators. Students’ experiences should focus on visual fraction models rather than algorithms. When tested, models may or may not be included. Students should learn to draw fraction models to help them compare and use reasoning skills based on fraction benchmarks. Students must also recognize that they must consider the size of <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the whole when comparing fractions (ie,1/2 and 1/8 of two medium pizzas is very different from1/2 of one medium and 1/8 of one large). Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> = 3/4 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">= 1/2

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">=1/3

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Use patterns blocks. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">1. If a red trapezoid is one whole, which block shows 1/3? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">2. If the blue rhombus is 1/3, which block shows one whole? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">3. If the red trapezoid is one whole, which block shows 2/3?

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Mary used a 12 x 12 grid to represent 1 and Janet used a 10 x 10 grid to represent 1. Each girl shaded grid <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">squares to show 1/4. How many grid squares did Mary shade? How many grid squares did Janet shade? Why did <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">they need to shade different numbers of grid squares? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Possible solution: Mary shaded 36 grid squares; Janet shaded 25 grid squares. The total number of little <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">squares is different in the two grids, so 1/4 of each total number is different.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">There are two cakes on the counter that are the same size. The first cake has ½ of it left. The second cake has 5/12 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">left. Which cake has more left?

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Misconceptions: (4.NF.1-2) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students think that when generating equivalent fractions they need to multiply or divide either the numerator or denominator, such as, changing 1/2 to sixths. They would multiply the denominator by 3 to get 1/6, instead of multiplying the numerator by 3 also. Their focus is only on the multiple of the denominator, not the whole fraction. It’s important that students use a fraction in the form of one such as 3/3 so that the numerator and denominator do not contain the original numerator or denominator.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍I can...
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can understand the value of a fraction. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can understand how a fraction model represents a fraction. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can understand how two fractions are equivalent. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can understand how two different looking fracton models are equal to the same value. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can recognize that two fractions with the same denominator and different numerators have a different value. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can use the symbols >, <, = to compare the value of fractions with same denominator and different numerators. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can recognize that two fractions with different denominators and same numerators represent different values. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can use the symbols >, <, or = to compare the value of fractios with different denominator and same numerators. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can determine whether a fraction is greater than, less than, or equal to a benchmark fraction. ( 1/4, 1/2, 3/4, 1/10) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can recognize that I can only compare 2 fractions when both fractions refer to the same whole. (using pattern blocks-hexagon = 1, so trapezoid = 1/2)

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Sample Assessments
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Fraction Quizzes <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Understanding Fractions Quiz

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Intervention:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Fraction Tiles/Pizza, Tangram shapes, Grid Paper, Choice Boards, ELL/EC students: vocabulary list ahead of time, Post words with visuals on word wall and in vocabulary notebooks, Use Frayer Models and foldables, Dominoes, Have students work in partners to divide the class into a given number of ways. Use egg cartons & counters to represent fractions. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">DPI Classroom Strategies p. 22

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Letter R--Have students work in groups to make fraction/decimal dominoes. One end has a picture; the other has the fraction and/or decimal notation. On the other side they could write the number/fraction out in word or expanded form and they could also write a story problem.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">DPI Classroom Strategies pg 25—Letter AA Play Buckets & Bowls ---Label containers Near Zero, About ½ and Close to 1. Pass out index cards with decimal numbers. Students would work with partners to convert the decimal to a fraction and place your card in the correct bucket.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Enrichment:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://daretodifferentiate.wikispaces.com/Choice+Boards <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Learning Logs

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Read The Hershey’s Milk Chocolate Bar Fraction Book by Pallotta to introduce fractions during reading. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students create a picture book of fractions to aid them in teaching younger siblings about fractions.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students write in their journal how they could share lunch with two or friends (Or) write how knowing fractions helps you play a musical instrument. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Illuminations Fraction Models <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Illuminations Equivalent Fractions

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Fraction Lessons

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Farmer Fred
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Delightfully Different Fractions

===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Notes and Additional Information ===